Set of supplementary notes.

8.3. SOLAR CELL 111
them separately for holes and electrons, focussing first on the holes, because their positive
charge simplifies matters slightly.
Drift or generation current: On the n-type side of the depletion region, the majority
carriers are electrons, but detailed balance ((7.12)) means that there will always be some small
density of minority holes. Any minority carrier wandering into the depletion regime will be
swept into the p-type region by the in-built junction field (Fig. 8.7). This generates a current
(from n to p, and therefore in the reverse direction) 2
−J gen
h
(8.2)
It does not depend strongly on the external bias V , because of the large inbuilt potential drop
in the depletion regime.
Diffusion or recombination current: . The holes in the p-type region, which are the
majority carriers there, have a small probability of being thermally excited up the potential
hill into the n-type region (Fig. 8.7). More strictly speaking, we need the number of holes with
energy at least eφ j from the band edge, because these will find states with equal energy on the
other side of the junction. Since the temperature is low compared to the height of the junction
potential, this current is activated, and in the presence of a bias voltage V takes the form
J rec
h
∝ e −e(φ b−V )/k B T
. (8.3)
Net current: We know that in equilibrium at zero bias the hole recombination current and
generation currents must cancel. Then the total hole current takes the form
h = J gen
h
(e eV/k BT − 1) . (8.4)
Electrons. The same analysis appplies to electrons, except that the corresponding electron
generation and recombination (number) currents flow in the opposite directions to their hole
counterparts. But electrons are oppositely charged, so the electrical current density has the
same form as (8.4).
Diode IV characteristic. The sum of the contributions of electrons and holes gives an
asymmmetrical form
I = I sat
(
e
eV/k B T − 1 ) (8.5)
where the saturation current I sat is proportional to n 2 i
e −Eg/kBT (see footnote 2).
and therefore of the Arrhenius form
8.3 Solar cell
If light shines on a p-n junction, without an external bias voltage, then each absorbed photon
will create an electron-hole pair (Fig. 8.9). If these carriers reach the junction, the built-in field
2 The magnitude can be estimated to be (n 2 i /N d)(L p /τ p ), where the first factor in brackets is the minority
hole density in the n-type region ((7.13)) τ p is the recombination time of a carrier, and L p is the length that
the hole will diffuse before it recombines with an electron